Theorem tpcomb 4760

Description: Swap 2nd and 3rd members of an unordered triple. (Contributed by NM, 22-May-2015.)

Assertion

Ref	Expression
tpcomb	⊢ {𝐴, 𝐵, 𝐶} = {𝐴, 𝐶, 𝐵}

Proof of Theorem tpcomb

Step	Hyp	Ref	Expression
1		tpcoma 4759	. 2 ⊢ {𝐵, 𝐶, 𝐴} = {𝐶, 𝐵, 𝐴}
2		tprot 4758	. 2 ⊢ {𝐴, 𝐵, 𝐶} = {𝐵, 𝐶, 𝐴}
3		tprot 4758	. 2 ⊢ {𝐴, 𝐶, 𝐵} = {𝐶, 𝐵, 𝐴}
4	1, 2, 3	3eqtr4i 2764	1 ⊢ {𝐴, 𝐵, 𝐶} = {𝐴, 𝐶, 𝐵}

Syntax hints:   = wceq 1534  {ctp 4637

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2697

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3or 1085  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2704  df-cleq 2718  df-clel 2803  df-v 3464  df-un 3952  df-sn 4634  df-pr 4636  df-tp 4638

This theorem is referenced by:  f13dfv  7288  frgr3v  30208  signswch  34407  signstfvcl  34419  dvh4dimN  41146